Rain water has (practically) no electrolytes. We've all heard that rainwater is acidic, but realistically, that is only relevant on a larger, ecological scale (tons of slightly acidic water will cause erosion). More importantly, rainwater will contain nitrates, oils, and other organic chemicals, and rainwater will contain lots of microorganisms, which will be difficult to filter out with an ordinary (ground-water) filtration system. Common ground-water filters are between 5 and 20 microns. Filtering water is extremely helpful for removing bacteria, but the water is still not sterile. Holding the rainwater may allow growth of bacteria, if the rainwater is "nutrient" rich.
The earth filters out nutrients and bacteria. It's not a perfect system, but groundwater is drinkable (usually after basic filtering). Rainwater should not be poured directly into ground water. Keeping the systems isolated would keep contamination minimalized. In terms of cost, try to think of this as rainwater will pollute the groundwater and could possibly ruin the well. Rainwater treatment can make it potable/drinkable, but I would reserve that option for the worst case scenario unless you have a good treatment system.
At a minimum, rainwater treatment (to make it potable) should include coarse and fine (5 micron) filtration, chlorine and UV sterilization, and carbon filtration.
I would do this:
Rain water (in order of priority)
Ground water (in order of priority)
The list is prioritized such that if groundwater is low, then laundry could be done with rainwater. If things get bad, you could use rainwater for bathing. I would try to avoid washing dishes and cooking with rainwater. I would drink rainwater if my life depended on it.